Summary

When we limit RT analysis to strong left and right handers with EHI scores of +-100, the critical three-way interaction effect is stronger (23.51ms, 95% CI [7.10, 39.92], p = .0025, one-sided), and left handers’ LVF global bias is closer to zero (4.59ms (95% CI [-7.80, 16.98]; the effect for right handers is 28.10ms, 95% CI [17.34, 38.86]). We still see a null result for accuracy, but the point estimates are now in the predicted direction (OR = 1.10, 95% CI [0.75, 1.61], p = .32, one-sided; where OR < 1 means greater LVF global bias for left handers).

Analyses

Demographics

Demographics for included participants, by handedness group (EHI bins).

Handedness N Age (years) Education (years) Sex (M/F/O) EHI
Left 138 30.07 (5.87) 14.68 (2.45) 81/56/1 -100 (0)
Mixed 524 28.55 (5.99) 14.31 (2.48) 264/250/10 -0.19 (63.85)
Right 182 29.87 (6.14) 14.34 (2.48) 96/85/1 100 (0)
Left: (EHI = -100) | Right: (EHI = +100) | Mixed: Everyone in between


Field x Level x Handedness (binned)

Do we find an interaction of field x level x handedness, when handedness is binned as left (EHI = -100) or right (EHI = +100)?

Summary. For reaction time, we find the critical interaction in the predicted direction (23.51ms, 95% CI [7.10, 39.92], p = .0025, one-sided). Left handers show 4.59ms LVF global bias (95% CI [-7.80, 16.98]), and right handers 28.10ms (95% CI [17.34, 38.86]). Mixed handers (not included in the categorical interaction analysis) show a LVF global bias of 24.195ms (95% CI [17.82, 30.58]).

For accuracy, we find no significant interaction of field by level by handedness (OR = 1.10, 95% CI [0.75, 1.61], p = .32, one-sided; where OR < 1 means greater LVF global bias for left handers). Point estimates of LVF global bias hardly differ between left handers (OR = 1.67, 95% CI [1.26, 2.22]) and right handers (OR = 1.84, 95% CI [1.42, 2.38]). For mixed handers (not included in the categorical interaction analysis), the point estimate is 1.67 (95% CI [1.44, 1.93]).



Reaction time

Plots

Error bars show 95% CI. Left handers are those with EHI = -100; Right handers, EHI = +100. “Mixed handers” are everyone with EHI values in between -100 and +100.



Statistics

Simple mixed regression model

Reaction time is modeled as a linear effect of field, level, and handedness, using data from every target-present trial with a “go” response:

lmer( rt ~ field*level*handedness + (1 | subject) )


Field by level by handedness interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
9 526,319.708 526,396.837 −263,150.854 526,301.708 - - -
10 526,313.82 526,399.519 −263,146.91 526,293.82 7.888 1 .005
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by handedness interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Right - Left 23.514 8.373 Inf 7.104 39.924 2.808 .005
1 A positive number means LVF global bias is stronger in right handers (as predicted by AAH)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


LVF Global bias by handedness bin (RT)
field_consec level_consec handedness estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Left 4.587 6.322 Inf −7.804 16.979 0.726 .468
LVF - RVF Local - Global Right 28.101 5.489 Inf 17.343 38.86 5.119 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided, uncorrected


LVF Global bias by handedness bin, including mixed (RT)
field_consec level_consec handedness estimate1 SE df2 asymp.LCL3,4 asymp.UCL3,4 z.ratio p.value5
LVF - RVF Local - Global Left 4.587 6.349 Inf −7.856 17.03 0.723 .47
LVF - RVF Local - Global Mixed 24.195 3.255 Inf 17.815 30.575 7.433 <.0001
LVF - RVF Local - Global Right 28.101 5.512 Inf 17.298 38.904 5.098 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Left: EHI = -100; Right: EHI = +100; Mixed: Everyone else. These mixed handers were not included in the model.
5 Two-sided, uncorrected


LVF Global bias by handedness bin, including mixed (RT)
field_consec level_consec handedness estimate1 SE df2 asymp.LCL3,4 asymp.UCL3,4 z.ratio p.value5
LVF - RVF Local - Global Strong Left 4.587 6.348 Inf −7.855 17.03 0.723 .47
LVF - RVF Local - Global Weak Left 24.329 4.389 Inf 15.728 32.93 5.544 <.0001
LVF - RVF Local - Global Weak Right 23.976 4.853 Inf 14.463 33.489 4.94 <.0001
LVF - RVF Local - Global Strong Right 28.101 5.512 Inf 17.298 38.904 5.098 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Strong left: EHI = -100; Weak left: -100 < EHI <= 0; Weak right: 0 < EHI < +100; Strong right: EHI = +100. These mixed handers were not included in the model.
5 Two-sided, uncorrected


Global bias by field, by handedness bin (RT)
level_consec field handedness estimate1 SE df2 z.ratio p.value3
Local - Global RVF Left 19.678 4.479 Inf 4.393 <.0001
Local - Global LVF Left 24.265 4.468 Inf 5.43 <.0001
Local - Global RVF Right 5.732 3.89 Inf 1.473 .141
Local - Global LVF Right 33.834 3.875 Inf 8.731 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Two-sided, uncorrected


RT (ms) by field, level and handedness bin
field level handedness emmean SE df1 asymp.LCL2 asymp.UCL2
RVF Global Left 662.211 14.833 Inf 633.139 691.283
LVF Global Left 639.53 14.828 Inf 610.468 668.592
RVF Local Left 681.889 14.842 Inf 652.799 710.979
LVF Local Left 663.795 14.844 Inf 634.702 692.889
RVF Global Right 701.166 12.916 Inf 675.851 726.48
LVF Global Right 686.623 12.91 Inf 661.319 711.927
RVF Local Right 706.898 12.921 Inf 681.573 732.223
LVF Local Right 720.457 12.922 Inf 695.13 745.783
1 Z-approximation
2 Confidence level: 95%



Field by level interaction (RT)
Old-school Omnibus F-test
term df sumsq meansq statistic p.value
field 1 792,986.103 792,986.103 11.227 .0008
level 1 4,085,669.668 4,085,669.668 57.843 <.0001
handedness 1 16,819,585.24 16,819,585.24 238.126 <.0001
field:level 1 749,826.902 749,826.902 10.616 .001
field:handedness 1 975,533.562 975,533.562 13.811 .0002
level:handedness 1 7,079.075 7,079.075 0.1 .752
field:level:handedness 1 318,410.828 318,410.828 4.508 .034
Residuals 38,935 2,750,103,740.474 70,633.203 - -
 



summary(rt_model_2bins)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field * level * handedness + (1 | subject)
##    Data: aah_for_rt_model_2bins
## 
## REML criterion at convergence: 526252.9
## 
## Scaled residuals: 
##       Min        1Q    Median        3Q       Max 
## -4.899514 -0.587954 -0.155036  0.379780  7.706435 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  subject  (Intercept) 28996.0  170.282 
##  Residual             41783.5  204.410 
## Number of obs: 38943, groups:  subject, 320
## 
## Fixed effects:
##                                      Estimate Std. Error  t value
## (Intercept)                         662.21065   14.83289 44.64475
## fieldLVF                            -22.68059    4.43112 -5.11847
## levelLocal                           19.67803    4.47932  4.39308
## handednessRight                      38.95491   19.66808  1.98062
## fieldLVF:levelLocal                   4.58721    6.32234  0.72556
## fieldLVF:handednessRight              8.13809    5.87303  1.38567
## levelLocal:handednessRight          -13.94567    5.93288 -2.35057
## fieldLVF:levelLocal:handednessRight  23.51411    8.37274  2.80841
## 
## Correlation of Fixed Effects:
##             (Intr) fldLVF lvlLcl hnddnR flLVF:L fLVF:R lvlL:R
## fieldLVF    -0.151                                           
## levelLocal  -0.149  0.498                                    
## hnddnssRght -0.754  0.114  0.112                             
## fldLVF:lvlL  0.105 -0.701 -0.707 -0.080                      
## fldLVF:hndR  0.114 -0.754 -0.376 -0.151  0.529               
## lvlLcl:hndR  0.112 -0.376 -0.755 -0.149  0.534   0.499       
## fldLVF:lL:R -0.080  0.529  0.534  0.106 -0.755  -0.701 -0.708


Accuracy

Plots

Error bars show 95% CI. Left handers are those with EHI = -100; Right handers, EHI = +100. “Mixed handers” are everyone with EHI values in between -100 and +100.


Statistics

Simple mixed regression model

Accuracy is modeled as a binomial effect of field, level, and handedness, using binary correct/incorrect data from every target-present trial:

glmer( correct ~ field*level*handedness + (1 | subject), family = "binomial" )


Field by level by handedness interaction (Accuracy)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
8 14,746.416 14,815.379 −7,365.208 14,730.416 - - -
9 14,748.19 14,825.773 −7,365.095 14,730.19 0.226 1 .634
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by handedness interaction (Accuracy)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec odds.ratio1 SE df2 asymp.LCL3 asymp.UCL3 null z.ratio p.value4
LVF / RVF Global / Local Right / Left 1.1 0.215 Inf 0.751 1.613 1 0.489 .625
1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF for right handers (predicted by AAH)
2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp.
3 Confidence level: 95%
4 Two-sided


LVF Global bias by handedness bin (Accuracy)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness odds.ratio1 SE df2 asymp.LCL3 asymp.UCL3 null z.ratio p.value4
LVF / RVF Global / Local Left 1.671 0.242 Inf 1.258 2.22 1 3.546 .0004
LVF / RVF Global / Local Mixed 1.668 0.124 Inf 1.442 1.93 1 6.876 <.0001
LVF / RVF Global / Local Right 1.842 0.242 Inf 1.423 2.384 1 4.64 <.0001
1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF, as predicted for right handers. Mixed handers' global bias is shown here, but their data was not included in the binomial model.
2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp.
3 Confidence level: 95%
4 Two-sided 



summary(acc_model_2bins)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
##    Data: aah_for_acc_model_2bins
## 
##      AIC      BIC   logLik deviance df.resid 
##  14748.2  14825.8  -7365.1  14730.2    40951 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -11.749323   0.116289   0.168889   0.247757   0.836170 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.02035  1.01012 
## Number of obs: 40960, groups:  subject, 320
## 
## Fixed effects:
##                                        Estimate Std. Error  z value
## (Intercept)                           3.0553598  0.1098501 27.81390
## fieldLVF                             -0.0683805  0.0854800 -0.79996
## levelGlobal                           0.4950481  0.0964275  5.13389
## handednessRight                       0.1251428  0.1452307  0.86168
## fieldLVF:levelGlobal                  0.5130782  0.1447220  3.54527
## fieldLVF:handednessRight              0.0264166  0.1159943  0.22774
## levelGlobal:handednessRight          -0.1367240  0.1288284 -1.06129
## fieldLVF:levelGlobal:handednessRight  0.0954962  0.1951619  0.48932
##                                           Pr(>|z|)    
## (Intercept)                             < 2.22e-16 ***
## fieldLVF                                0.42373447    
## levelGlobal                          0.00000028382 ***
## handednessRight                         0.38886230    
## fieldLVF:levelGlobal                    0.00039221 ***
## fieldLVF:handednessRight                0.81984824    
## levelGlobal:handednessRight             0.28855899    
## fieldLVF:levelGlobal:handednessRight    0.62461684    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF    -0.400                                           
## levelGlobal -0.348  0.453                                    
## hnddnssRght -0.740  0.302  0.264                             
## fldLVF:lvlG  0.237 -0.589 -0.664 -0.179                      
## fldLVF:hndR  0.294 -0.736 -0.333 -0.408  0.433               
## lvlGlbl:hnR  0.261 -0.338 -0.747 -0.363  0.496   0.458       
## fldLVF:lG:R -0.175  0.436  0.491  0.243 -0.740  -0.592 -0.658